Question: Simplify; express your answer in exponential form. Assume $x\neq 0, k\neq 0$. $\dfrac{{(x^{5})^{-5}}}{{(xk^{-5})^{3}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{5}}$ to the exponent ${-5}$ . Now ${5 \times -5 = -25}$ , so ${(x^{5})^{-5} = x^{-25}}$ In the denominator, we can use the distributive property of exponents. ${(xk^{-5})^{3} = (x)^{3}(k^{-5})^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{5})^{-5}}}{{(xk^{-5})^{3}}} = \dfrac{{x^{-25}}}{{x^{3}k^{-15}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{-25}}}{{x^{3}k^{-15}}} = \dfrac{{x^{-25}}}{{x^{3}}} \cdot \dfrac{{1}}{{k^{-15}}} = x^{{-25} - {3}} \cdot k^{- {(-15)}} = x^{-28}k^{15}$.